This invention is drawn to determining the total mass of very small samples. More particularly, the invention is drawn to absolute total mass determination using Compton and Rayleigh scattered radiation.
X-rays are electromagnetic radiation covering a range of wavelengths from a few hundredths to several tens of nanometers. X-rays are typically produced in sealed high vacuum tubes, where electrons generated from a hot cathode filament, for example, tungsten, are accelerated to a positive metal target anode causing the generation of x-rays. A typical spectral intensity distribution of x-rays emitted from an anode metal includes a series of characteristic lines and an accompanying broad band of radiation called the x-ray continuum or brehmsstrahlung caused by the deceleration of the electron beam in the anode.
As explained in Kirk-Othmer, Encyclopedia of Chemical Technology, Vol. 2, pages 623-634, John Wiley & Sons, New York, 1985, the origin of the characteristic lines are as follows. When the energy of an incident electron is greater than the binding energy of a core shell electron, there is a probability that an interaction between the two may occur such that the bound electron is ejected leaving the atom in an excited state. Electronic relaxation then occurs in which an electron from an outer shell fills the newly created vacancy. This process is accompanied by a release of energy in an amount corresponding to the difference between the initial and final states of the atom. The specific mechanism for the energy release for the purposes of this discussion is the emission of a characteristic x-ray photon. In the case of an initial K shell ionization filled by an L shell electron, the emitted x-ray is called a Ka photon.
One analytical use of x-rays is the determination of composition of samples. In an x-ray fluorescence experiment radiation from a standard x-ray tube is used to excite the atoms of a specimen causing fluorescence which is then analyzed by means of an x-ray spectrometer. As FIG. 1 illustrates, the instrument is composed basically of an evacuated chamber in which a sample 1 is held in a sample holder 2, and an x-ray tube 3 that provides a source of x-rays 4 therein. A collimator 5 operates to collimate the x-rays to produce incident x-ray 6 which impinges on sample 1. X-ray emissions 7 from the atoms of the sample are collimated by collimator 8 into a detector 9. Other components usually include a computing apparatus 10 for generating a spectrum and a power source 11 used to power x-ray tube 3.
Many things can happen to an x-ray as it enters the realm of an atom consisting of electrons and a nucleus. FIG. 2 diagrammatically illustrates the interaction of an electron 12 with an incident x-ray 13 of wavelength .lambda. or energy E=hc/.lambda., where h is Planck's constant and c is the speed of light. If the energy of incident x-ray 13 is sufficient, it will impart to electron 12 orbiting the nucleus energy large enough to overcome the energy binding the electron to the nucleus. This interaction can occur as if the electron 12 were moving essentially as a free particle and the nucleus did not exist. Billiard ball scattering occurs between incident x-ray 13 and electron 12 in the atom, and this occurs as if the atom were not there. After the collision, the recoiling electron 12 takes up some of the energy of incident x-ray 13, and the scattered x-ray 14 of necessity must have less energy than incident x-ray 13 to account for that gained by the electron 12 as a result of the collision. Because of this loss of energy by the incident x-ray, the process is called "inelastic" scattering, a process discovered by A. H. Compton in 1923, and is also known, therefore, as Compton scattering. This process generally occurs with high energy x-rays with corresponding high energy electron recoil. In the reverse case, where the incident x-ray has low energy and/or very low energy is given to the electron as compared with its binding energy, the process tends to occur not with each electron by itself but with the atom as a whole. The recoil energy is then carried off by the mass of the whole atom rather than just one electron which is kicked out of the atom. This recoil energy is very small for reasonable energy incident x-rays, and the net result is that there is no apparent energy loss to the incident x-ray, i.e., the scattered x-ray has essentially the same energy. This is called "elastic" scattering because there is no apparent energy loss to the incident x-ray, or Rayleigh scattering after its discoverer. Thus, in Rayleigh scattering the interaction of the x-ray is apparently with the whole atom, not just with an electron. Compton and Rayleigh scattering are the two primary forms of scattering that effect x-rays passing through atoms of samples.
Formerly, scatter was regarded only as a nuisance in x-ray fluorescence experiments. Background in these experiments is mostly scattered primary radiation, and both Rayleigh and Compton scatter target lines complicate the emission spectrum obtained from samples and increase the possibility of spectral-line interference. However, scattered x-rays have more recently proved beneficial in many ways. Several analytical methods are based on x-ray scatter rather than emission, including methods for determining carbon in hydrocarbons. See E. P. Bertin, Principles and Practice of X-ray Spectrometric Analysis, Second Edition, Plenum Press, New York, 1975.
It is also known that the Compton scatter cross section (in sq cm/gm), also known as the mass scattering coefficient, will decline by approximately a factor of two from low atomic number (Z) elements (e.g., carbon, Z=6) to high atomic number elements (e.g., lead, Z=82), while the Rayleigh scattering cross-section increases with atomic number (z). However, the Compton scatter cross section is often assumed to be approximately constant at a given energy and scattering angle for the entire periodic table of elements (except hydrogen) in order to not unduly complete the analysis. See for example R. Tertian and F. claisse, Principles of Quantitative X-Ray Fluorescence Analysis, Heyden & Son LTD, London, 1982, pages 30-31.
This dependence of the Compton cross section or scattering probability upon the atomic number is often disregarded, or considered constant; although approximately true, it is not entirely accurate for two reasons. First, the mass scattering coefficient for Compton scattering decreases by as much as a factor of two from low atomic number elements to higher atomic number elements. This trend continues, and becomes greater, as higher atomic numbered elements are encountered. Accordingly, correction must be made for this atomic number dependence of the Compton scattering cross section as a function of the elemental composition of the sample being measured if an absolute measurement of the mass of the sample is to be determined.
Although the relative compositional analysis of samples using Compton scattering is known (e.g., see U.S. Pat. No. 4,117,935), no known device or attempt has been made to use Compton scattering to determine total absolute mass of samples. Previous methods of mass measurement of very low mass in a laboratory setting include hanging a sample attached to a plastic support from a quartz fiber. The rotation of the fiber is indicative of the mass of the sample. Unfortunately, the determination of mass by this method suffers from electrostatic effects on the plastic, and the sensitivity (lowest mass measurable) is only about 0.1 microgram. Also, these prior art microbalances can only tare out about 1 gram. If the sample plus sample holder weighs much more than this, for example, 2 grams, the scale will not be able to determine mass of samples in the microgram range. If the sample holder includes a thin film of plastic upon which the sample is placed, it is not possible to weigh the sample holder and film plus sample, wipe the sample off the film, then weigh the sample holder plus film and obtain a net weight for the sample, since the weight of the sample holder is much higher than the maximum tare weight. In practice, the thin film breaks upon wiping, so that this procedure is not only not possible but also not practical. If a thicker film is used to avoid this latter problem, accuracy is lost because one is then trying to measure mass on the order of micrograms on top of several hundred micrograms of plastic film. Further, the plastic, as mentioned previously, electrostatically charges, affecting accuracy.
Frequently in many scientific disciplines (e.g., geology, mineralogy) it is necessary to know the mass of very small samples (down to 10 nanograms) for normalization purposes, especially if the sample is fairly large in area compared to the area of relatively uniform flux density radiation incident upon the sample, or for calculating the absorption of low energy fluorescent radiation by the sample itself. It would be advantageous if a method and device could be designed which could measure the total mass of very small samples in the range of from about 10 milligrams to about 100 nanograms while avoiding the disadvantages of previous methods.